Clicker Summary

Physics 122 Winter 2013

D. Hertzog

Clicker 1-1

Q2 Q1

x

y

g q

A charged ball Q1 is placed next to another charged ball

Q2 which is connected to a string. Q2 comes to

equilibrium at angle q as shown.

–What is the sign of FEx ?

A) FEx < 0

B) FEx > 0

C) Cannot determine sign of FEx from this information

Clicker 1-2

Q2 Q1

x

y

g q

A charged ball Q1 is placed next to another charged ball

Q2 which is connected to a string. Q2 comes to

equilibrium at angle q as shown.

–What is the sign of FEy ?

A) FEy < 0

B) FEy > 0

C) Cannot determine sign of FEy from this information

Clicker 1-3 Q2

Q1

g

d12

Q2

d23

Q3

A) The charge of Q3 has the same sign of the charge of Q1

B) The charge of Q3 has the opposite sign as the charge of Q1

C) Cannot determine the relative signs of the charges of Q3 & Q1

A charged ball Q1 is fixed to a horizontal surface.

Another charged ball Q2 is brought near

It achieves equilibrium at a distance d12 above Q1.

Q1 is replaced by Q3, and

Q2 achieves equilibrium at d23 (< d12)

Clicker 1-4 Q2

Q1

g

d12

Q2

d23

Q3

A) The magnitude of charge Q3 < the magnitude of charge Q1

B) The magnitude of charge Q3 > the magnitude of charge Q1

C) Cannot determine relative magnitudes of charges of Q3 & Q1

A charged ball Q1 is fixed to a horizontal surface.

Another charged ball Q2 is brought near

It achieves equilibrium at a distance d12 above Q1.

Q1 is replaced by Q3, and

Q2 achieves equilibrium at d23 (< d12)

Lecture 2

Clicker 2-1

Two equal mass balls are suspended from the ceiling with equal length nonconducting threads as shown. Ball 1 has charge Q1 = +3q and Ball 2 has charge Q2 = +q.

– Which of the following pictures best represents the equilibrium position?

Q2

Q1

(a)

+3q +q

Q2 Q1

(b)

+3q +q Q2 Q1

(c)

+3q +q

Clicker 2-2

What happens to the Force on q1 if its sign is changed?

A) |F1| increases

B) |F1| remains the same

C) |F1| decreases

D) Need more information to determine

q1

q2

q3

q4

• Two charges, Q1 and Q2 , fixed along the x-axis as shown, produce an electric field E at a point (x,y) = (0,d) which is directed along the negative y-axis.

– Which is true?

(a) Both charges Q1 and Q2 must be positive.

(b) Both charges Q1 and Q2 must be negative.

(c) The charges Q1 and Q2 must have opposite signs.

Q2 Q1 x

y

E d

Clicker 2-3

• Q1 has charge +Q

• Q2 has charge +2Q

• They are separated by d.

• Charge q is a distance a away from Q1

Is there a place – the value for a -- between Q1 and Q2 where the

force on ANY charge (positive or negative) is zero?

(a) NO

(b) Yes, but I can’t find it with all this time pressure.

(c) Yes and my answer is _______ from Q1. I will volunteer to

specify if you ask me Clicker 2-4

12 d

d a

What is the direction of the electric field at point

P, the unoccupied corner of the square?

d

d

q +q

+q

A) B) C) D) Need to know d

Need to

know d & q E) 0E

P

Clicker 2-5

Lecture 3

Consider a point charge fixed at the origin of a co-ordinate

system as shown.

Which of the following graphs best represents the

functional dependence of the Electric Field?

Q

y

r

f

Er

Clicker 3-1

Consider a point charge fixed at the origin of a co-ordinate

system as shown.

Which of the following graphs best represents the

functional dependence of the Electric Field?

Q

y

r

f

Ex

Clicker 3-2

Clicker

a

a

+Q

x

y

-Q

a

2a

(a) Ex(2a,a) < 0 (b) Ex(2a,a) = 0 (c) Ex(2a,a) > 0

E Consider a dipole aligned with the y-

axis as shown.

Which of the following statements

about Ex(2a,a) is true?

Clicker 3-3

Examine the electric field lines produced by the

2 charges in this figure.

Which statement is true?

(a) q1 and q2 have the same sign

(b) q1 and q2 have the opposite signs and q1 > q2

(c) q1 and q2 have the opposite signs and q1 < q2

q1 q2

Clicker 3-4

Lecture 4

Consider a circular ring with a uniform charge distribution

(l charge per unit length). The total charge of this ring is +Q.

The electric field at the origin is

(a) zero

R

x

y

+ + + +

+ +

+ + +

+ +

+ + + + + + + + + +

+

(b) (c)

Clicker 4-1

An electron is fired upward at speed v0 toward the top of the page as shown. A uniform electric field points to the right.

Which trajectory best represents its motion:

(A) (B) (C) (D) (E)

Clicker 4-2

An electric dipole consists of two equal and opposite charges, fixed a distance 2a apart. It is placed in a uniform electric field as shown. It will

A. Not translate in any direction

B. Translate horizontally

C. Translate vertically

D. Start to rotate clockwise

E. Start to rotate counter-clockwise

Clicker 4-3

Imagine a cube of side a positioned in a region of constant electric field as shown.

– Which of the following statements about the electric flux FE through the surface of this cube is true?

(a) FE = 0 (b) FE 2a2 (c) FE 6a2 a

a

Clicker 4-4

Consider 2 spheres (of radius R and 2R)

drawn around an electric dipole

Which of the following statements about the net electric

flux through the 2 surfaces (F2R and FR) is true?

(a) FR < F2R (b) FR = F2R (c) FR > F2R

Clicker 4-5

Lecture 5

Compare the electric field at point X to the one

you would find if the conducting shell was

removed.

A Q = -3 mC charge is surrounded by an uncharged conducting spherical shell (in yellow)

(a) Eshell < ENoShell (b) Eshell = ENoShell (c) Eshell > ENoShell

s2

s1

-Q

X

Clicker 5-1

Clicker 5-2

What is the value of the surface

charge density s1 on the inner

surface of the conducting shell?

A Q = -3 mC charge is surrounded by an uncharged conducting spherical shell (in yellow) s2

s1 r1

-Q

r2

(a) s1 = -Q (b) s1 = +Q (c) s1 = 0 (d) s1 = −𝑄

4𝜋𝜀0𝑟12 (e) s1 =

+𝑄

4𝜋𝜀0𝑟12

Clicker 5-3

A line charge l C/m is placed along the axis of an uncharged conducting cylinder of inner radius ri = a, and outer radius ro = b as shown.

What is the value of the charge density so (C/m2) on the outer surface of the cylinder?

(a) (b) (c)

l a

b

Lecture 6

Clicker 6-1

A B C D E

A long thin wire has a uniform positive charge density of 2.5 C/m. Concentric with the wire is a long thick conducting cylinder, with inner radius 3 cm, and outer radius 5 cm. The conducting cylinder has a net linear charge density of 4 C/m.

What is the linear charge density of the induced charge on the inner surface of the conducting cylinder li and on the outer surface lo?

li: +2.5 C/m 4 C/m 2.5 C/m 2.5 C/m 0

lo: 6.5 C/m 0 +2.5 C/m 1.5 C/m 4 C/m

li

lo

A particle with charge +Q is placed in the center of an uncharged conducting hollow sphere. How much charge will be induced on the inner and outer surfaces of the sphere?

A) inner = Q, outer = +Q

B) inner = Q/2 , outer = +Q/2

C) inner = 0, outer = 0

D) inner = +Q/2, outer = Q/2

E) inner = +Q, outer = Q

Qinner

Qouter

Q

Clicker 6-2

You hold a positively charged ball and walk to the right in a region

that contains an electric field directed to the left.

WH is the work done by the hand on the ball

WE is the work done by the electric field on the ball

Which of the following statements is true:

A) WH > 0 and WE > 0

B) WH > 0 and WE < 0

C) WH < 0 and WE < 0

D) WH < 0 and WE > 0

E dr

Clicker 6-3

In Case A two negative charges which are equal in magnitude are separated by a distance d. In Case B the same charges are separated by a distance 2d. Which configuration has the highest potential energy?

•A) Case A

•B) Case B d

2d

Case A

Case B

Clicker 6-4

What is the total energy required to bring in three identical charges, from

infinitely far away to the points on an equilateral triangle shown.

A) 0

B)

C)

D)

E)

d

QU

1

4 0

2

d

QU

1

42

0

2

d

QU

1

43

0

2

d

QU

1

46

0

2

d

d d

Q

Q

Q

Clicker 6-5

Lecture 7

Suppose one of the charges is negative. Now what is the total

energy required to bring the three charges in infinitely far away?

A) 0

B)

C)

D)

E)

d

QU

1

41

0

2

+

d

QU

1

41

0

2

d

QU

1

42

0

2

d

QU

1

42

0

2

+

Q Q

Q

d

d d

Clicker 7-1

Lecture 8

A point charge Q is fixed at the center of an uncharged conducting spherical shell of inner radius a and outer radius b.

– What is the value of the potential Va at the inner surface of the spherical shell?

a

b

Q

1A

(c) (b) (a)

Clicker 8-1

At which point is the direction of the E field along the negative x axis ?

A B C D E = none of these

Clicker 8-2

What is the sign of WAC work done by E field to move negative charge from A to C ?

A) WAC < 0 B) WAC 0 C) WAC > 0

Clicker 8-3

Lecture 9

Two test charges are brought separately to the vicinity of positive charge Q.

– Charge +q is brought to A, a distance r from Q.

– Charge + 2q is brought to B, a distance 2r from Q.

– Compare the potential at A (VA) to that at B:

(a) VA < VB (b) VA = VB (c) VA > VB

Q

A q

r

Q

B 2q 2r

Clicker 9-1

A positive charge Q is moved from A to

B along the path shown. What is the

sign of the work done to move the

charge from A to B?

(a) WAB < 0 (b) WAB = 0 (c) WAB > 0

2B

A B

Clicker 9-2

An electric dipole with charge magnitude Q and separation 2d

is oriented as shown below. Compare VA, the electric potential

at point A, with VB, the electric potential at point B.

(a) VA < VB (b) VA = VB (c) VA > VB

Clicker 9-3

Which of the following charge distributions produces V(x) = 0 for all points

on the x axis? ( we are defining V(x) 0 at x = )

(a)

x

+2mC

-2mC

+1mC

-1mC (b)

x

+2mC

-1mC

+1mC

-2mC (c)

x

+2mC

-1mC

-2mC

+1mC

Clicker 9-4

x

+s

x = 0 a b

Con

ducting s

lab

Which curve best represents the Potential in

the positive x direction?

Clicker 9-5

Lecture 10

Two “infinite” oppositely charged parallel plates are located at

–d and +d on the x axis. Which graphs best represent the

Electric Field and the Potential Difference vs x ?

Clicker 10-1

Clicker 10-2 Initial charge on capacitor Q0

+Q0

Q0

d

t d

+Q1

Q1

Insert uncharged conductor

Charge on capacitor now Q1

A) Q1 < Q0

B) Q1 Q0

C) Q1 > Q0

How is Q1 related to Q0 ?

What is the total charge induced on the bottom

surface of the conductor?

A) +Q0

B) Q0

C) 0

D) Positive but the magnitude is unknown

E) Negative but the magnitude is unknown

t d

+Q1

Q1

(Initial charge on capacitor Q0)

Clicker 10-3

A) Q1 < Qo B) Q1 Qo C) Q1 > Qo

Clicker 10-3

Potential difference is

the SAME as before.

(we adjusted it)

How is charge Q1 related to the original Q0 ?

Clicker 10-4

We adjusted Q1 to

make the Potential

Difference the Same

How did the Capacitance of the object change?

A) C1 > Co B) C1 Co C) C1 < Co

Lecture 11

a2

b

+Q -Q

a1

b

+Q

-Q

In each case below, a charge of +Q is placed on a solid spherical conductor and a charge of -Q is placed on a concentric conducting spherical shell.

– Let V1 be the potential difference between the spheres with (a1, b).

– Let V2 be the potential difference between the spheres with (a2, b).

– What is the relationship between V1 and V2?

(a) V1 < V2

(b) V1 = V2

(c) V1 > V2

Clicker 11-1

Suppose you have two identical capacitors, each having capacitance C.

Cmax is the biggest possible equivalent capacitance that can be made by

combining these two, and Cmin is the smallest.

How does Cmax compare to Cmin?

A. Cmax = 4Cmin

B. Cmax = 3Cmin

C. Cmax = 2Cmin

D. Cmax = (3/2)Cmin

E. Cmax = Cmin

Clicker 11-2

o

o

C C C Ceq

(a) Ceq = (3/2)C (b) Ceq = (2/3)C (c) Ceq = 3C

What is the equivalent capacitance, Ceq, of the combination shown?

Clicker 11-3

Which of the following is NOT necessarily true:

A) V0 V1

B) Ctotal > C1

C) V2 V3

D) Q2 Q3

E) V1 V2 + V3

Ctotal

C1

C2

C3

V0

V1 Q1

V2

Q2

V3 Q3

Clicker 11-4

Lecture 12

d d V 2d 2d V C1 C2

(a) U1 < U2 (b) U1 = U2 (c) U1 > U2 (d) I don’t know

• Two identical parallel plate capacitors are connected to a battery.

– What is the relation between U1, the energy stored in C1, and U2, the energy stored in C2?

– C1 is then disconnected from the battery and the separation between the plates of both capacitors is doubled.

Clicker 12-1

Consider two cylindrical capacitors, each of length L.

C1 has inner radius a and outer radius b.

C2 has inner radius 2a and outer radius 2b.

(a) U2 < U1 (b) U2 = U1 (c) U2 > U1 (d) I don’t know

If both capacitors are given the same amount of charge, what is

the relation between U1, the energy stored in C1, and U2, the

energy stored in C2?

a b

2a 2b

C1

C2

Clicker 12-2

a

b

LCCylinder

ln

2 0

• Two parallel plate capacitors are identical except C1 has half of the space between the plates filled with a material of dielectric constant k.

k C1

C2

E1=?

E2=?

+Q

+Q

-Q

-Q

– Both capacitors have charge Q

– Compare E1, the electric field in the air of

C1, to E2, the electric field in the air of C2

(a) E1 < E2 (b) E1 = E2 (c) E1 > E2 (d) I don’t know

Clicker 12-3

Lecture 13

•An air-gap capacitor, having capacitance C0 and width x0 is connected to a battery of voltage V.

•A dielectric k of width x0/4 is inserted into the gap as shown.

V C0

x0

What changes when the dielectric added?

A) Only C B) only Q C) only V D) C and Q E) V and Q F) I Don’t Know

k V

x0/4

Clicker 13-1

• Two cylindrical resistors, R1 and R2, are made of identical material. R2 has twice the length of R1 but half the radius of R1.

– These resistors are then connected to a battery V as shown:

V

I1 I2

– What is the relation between I1, the current flowing in R1 , and I2 , the current flowing in R2?

(a) I1 = I2 (b) I1 = 2I2 (c) I1 = 4I2 (d) I1 = 8I2

Clicker 13-2

Combine Resistances:

A) in series B) in parallel C) neither in series nor in parallel

R1 and R2 are connected:

30 second clicker

Clicker 13-3

Combine Resistances:

R2 and R4 are connected in series R24

R3 and R24 are connected in parallel R234

A) R234 1 W B) R234 2 W C) R234 4 W D) R234 6 W

What is the value of R234?

V

R1

R3 R24

In the circuit shown: V 18V,

R1 1W, R2 2W, R3 3W, and R4 4W.

What is V2, the voltage across R2?

Clicker 13-4

Lecture 14

R

12 V

12 V

R

12 V

I a

b

• Consider the circuit shown.

– The switch is initially open and the current flowing through the bottom resistor is I0.

– After the switch is closed, the current flowing through the bottom resistor is I1.

– What is the relation between I0 and I1?

(a) I1 < I0 (b) I1 = I0 (c) I1 > I0

Clicker 14-1

• Consider the circuit shown:

– What is the relation between Va -Vd and Va -Vc ?

(a) (Va -Vd) < (Va -Vc) (b) (Va -Vd) = (Va -Vc)

(c) (Va -Vd) > (Va -Vc)

12 V

I1 I2

a

b

d c

50W

20W 80W

Clicker 14-2

• Consider the circuit shown:

• What is the relation between I1 and I2?

12 V

I1 I2

a

b

d c

50W

20W 80W

(a) I1 < I2 (b) I1 = I2 (c) I1 > I2

Clicker 14-3

Lecture 15

a

b

R

C

II

R

At t = 0 the switch is thrown from position b to position a in the circuit shown: The capacitor is initially uncharged.

– What is the value of the current I0 just after the switch is thrown?

(a) I0 = 0 (b) I0 = /2R (c) I0 = 2/R

Clicker 15-1

a

b

R

C

II

R1B

(a) I = 0 (b) I = /2R (c) I > 2/R

What is the value of the current I

after a very long time?

Clicker 15-2

a

b

R

C

II

R

• At t = 0 the switch is thrown from position b to position a in the circuit shown: The capacitor is initially uncharged.

– At time t = t1= t, the charge Q1 on the capacitor is (1-1/e) of its asymptotic charge Qf=C.

– What is the relation between Q1 and Q2 , the charge on the capacitor at time t = t2= 2t?

(a) Q2 < 2 Q1 (b) Q2 = 2 Q1 (c) Q2 > 2 Q1

Clicker 15-3

• At t = 0 the switch is connected to position a in the circuit shown: The capacitor is initially uncharged.

– At t = t0, the switch is thrown from position a to position b.

– Which of the following graphs best represents the time dependence of the charge on C?

(a) (b) (c)

C

a b

R 2R

t

q

0

C

0 1 2 3 40

0.5

1

t/RC

Q f( )x

x

t0 t

q

0

C

0 1 2 3 40

0.5

1

t/RC

Q f( )x

x

t0 0 1 2 3 40

0.5

1

t/RC

Q f ( )x

x

q

0

C

tt0

Clicker 15-4

Lecture 16 - Review

Lecture 17

An electron enters a region of space with speed v and exits the

region as shown with the same speed (magnitude) v.

From this information, what can we infer about the Ey and Bz fields

in the region?

A. Only Ey exists B. Only Bz exists C. Both Ey & Bz can exist

Clicker 17-1

Two protons each move at speed v toward a region of space which contains a constant B field in the –z direction.

– What is the relation between the magnitudes of the forces on the two protons in the magnetic field region?

(a) F1 < F2 (b) F1 = F2 (c) F1 > F2

X X X X X X X X X X X X

B

x

y

z

1

2

Clicker 17-2

Two protons each move at speed v toward a region of space which contains a constant B field in the –z direction.

X X X X X X X X X X X X

B

x

y

z

1

2

2B

(a) F2x < 0 (b) F2x = 0 (c) F2x > 0

What is F2x, the x-component of the force on the

second proton?

Clicker 17-3

Clicker 17-4

Question about work; Answer = no work,

B

Lecture 18

A square loop of wire is carrying current in the counterclockwise direction. A horizontal uniform magnetic field points to the right

What is the force on section a-b of the loop ?

A) zero B) out of the page C) into the page D) Up E) Down

C: 18-1

A square loop of wire is carrying current in the counterclockwise direction. A horizontal uniform magnetic field points to the right

What is the force on section b-c of the loop ?

A) zero B) out of the page C) into the page D) Up E) Down

C: 18-2

A square loop of wire is carrying current in the counterclockwise direction. A horizontal uniform magnetic field points to the right

What is the force on section d-a of the loop ?

A) zero B) out of the page C) into the page D) Up E) Down

C: 18-3

x x x x x xx x x x x xx x x x x xx x x x x xx x x x x xx x x x x xx x x x x xx x x x x x

II

I

B

x

y A current I flows in a wire which is formed in the shape of an isosceles triangle as shown. A constant magnetic field exists in the -z direction.

What is Fy, net force on the wire in the y-direction?

(a) Fy < 0 (b) Fy = 0 (c) Fy > 0

C: 18-4

A circular loop of radius R carries current I. A constant magnetic field B exists in the +x direction. Initially the loop is in the x-y plane.

– How will the coil rotate?

C: 18-5

I

R

x

y B

(a) (b) (c) It will not rotate I

R

x

y B

I

R

x

y B

Lecture 19

A long straight wire is carrying current from left to right. Two identical charges are moving with equal speed. Compare the magnitude of the force on charge a moving directly to the right, to the magnitude of the force on charge b moving up and to the right at the instant shown (i.e. same distance from the wire). v

I

v (a)

r r

(b)

A) |Fa| > |Fb|

B) |Fa| |Fb|

C) |Fa| < |Fb|

C: 19-1

Two long wires carry opposite current

What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”?

A) Left B) Right C) Up D) Down E) Zero

x

x

C: 19-2

• A current I flows in the positive y direction in an infinite wire; a current I also flows in the loop as shown in the diagram.

– What is Fx, net force on the loop in the x-direction?

(a) Fx < 0 (b) Fx = 0 (c) Fx > 0

I

I

x

y

C: 19-3

Lecture 20

V

C

R

S L2

L1 A conducting rail of length L1 rests on the top of the circuit loop as shown. It is free to move. A uniform magnetic field exists in the box of dimension L2 by L3. When switch s is closed, which way does the rail move (if at all) ?

L3

rail

B

A) Left

B) Right

C) Rotates clockwise

D) Rotates counterclockwise

E) Does not move C: 20-1

V

C

R

S L2

L1 A conducting rail of length L1 rests on the top of the circuit loop as shown. It is free to move. A uniform magnetic field exists in the box of dimension L2 by L3. What is the magnitude of the force on the rail RC seconds after the switch has been closed?

L3

rail

B

A) 0.37(V/R) B) 0.63(VL1B)/R C) 0.37(VL1B)/R D) (V/R) L1L2B E) 0.37(VL2B)/R F) My answer wasn’t listed

C: 20-2

• A loop of wire is formed in this circuit as shown on the right of the drawing.

• We define the direction of positive current through the loop, +I, as shown

• What is the direction of the magnetic moment and current?

5V R

I

V

C: 20-3

A) I is > 0 & m is out of the page B) I is < 0 & m is out of the page C) I is > 0 & m is into the page D) I is < 0 & m is into the page

C: 20-4

x

y z

B

• Consider the loop of current shown,

which is located in a uniform vertical

magnetic field.

• About which axis might this loop rotate?

A) x B) y C) z D) It will not rotate

C: 20-5

3a

a

3a

I I

2a

Two cylindrical conductors each carry current I into the screen as shown. The conductor on the left is solid and has radius R = 3a. The conductor on the right has a hole in the middle and carries current only between R = a and R = 3a.

– What is the relation between the magnetic fields at R = 6a for the two cases (L=left, R=right)?

(a) BL(6a)< BR(6a) (b) BL(6a)= BR(6a) (c) BL(6a)> BR(6a)

C: 20-6

Two cylindrical conductors each carry current I into the screen as shown. The conductor on the left is solid and has radius R = 3a. The conductor on the right has a hole in the middle and carries current only between R = a and R = 3a.

(a) BL(2a)< BR(2a) (b) BL(2a)= BR(2a) (c) BL(2a)> BR(2a)

What is the relation between the magnetic field at R = 2a for the two cases (L=left, R=right)? (do the calculation)

3a

a

3a

I I

2a 2a

Lecture 21

• A conducting rectangular loop is accelerated in the +x direction through a region of constant magnetic field B in the -z direction as shown.

– What is the direction of the induced current in the loop?

(c) no induced current (a) ccw (b) cw

X X X X X X X X X X X X

X X X X X X X X X X X X

X X X X X X X X X X X XX X X X X X X X X X X X

v

x

y

a

C: 21-1

At what angle q is emf the largest?

A) q 0 B) q 45o C) q 90o D) emf is same at all angles

C: 21-2

Lecture 22

Suppose you double the magnetic field in a given region and

quadruple the area through which this magnetic field exists. The

effect on the flux through this area would be to

A. Leave it unchanged

B. Double it

C.Quadruple it

D. Increase by factor of 6

E. Increase it by factor of 8 C: 22-1

A 3.0-cm by 5.0-cm rectangular coil has 100 turns. Its axis

makes an angle of 55º with a uniform magnetic field of 0.35 T.

What is the magnetic flux through this coil?

A. 3.0 x 10–4 Wb

B. 4.3 x 10–4 Wb

C.3.0 x 10–2 Wb

D.4.3 x 10–2 Wb

E. 5.3 x 10–2 Wb C: 22-2

A conducting rectangular loop moves with constant velocity v in the -y direction and a constant current I flows in the +x direction as shown.

What is the direction of the induced current in the loop?

(a) ccw (b) cw (c) no induced current

v

I

x

y

C: 22-3

A loop rests in the xy plane. The z axis is normal to the plane. The direction of the changing flux is indicated by the arrow on the z axis. The diagram that correctly shows the direction of the resultant induced current in the loop is

B B B B B

B

increasing

B

increasing

B

decreasing

B

decreasing

B

increasing

A) B) C) D) E)

C: 22-4

Lecture 23

The magnetic field in a region of space of radius 2R is aligned with the z-direction and changes in time as shown in the plot.

Which way would the induced current flow in yellow loop at time t=t1?

C: 23-1

Field at t = 0

(a) ccw (b) cw (c) No current

What is the relation between the magnitudes of the induced electric fields ER at radius R and E2R at radius 2R ?

(a) E2R = ER (b) E2R = 2ER (c) E2R = 4ER

C: 23-2

• Consider the two inductors shown:

– Inductor 1 has length l, N total turns and has inductance L1.

– Inductor 2 has length 2l, 2N total turns and has inductance L2.

– What is the relation between L1 and L2?

(a) L2 < L1 (b) L2 = L1 (c) L2 > L1

C: 23-3

a

b

R

L

II

R

• At t = 0 the switch is thrown from position b to position a in the circuit shown:

– What is the value of the current I a long time after the switch is thrown?

(a) I = 0 (b) I = / 2R (c) I = 2 / R

C: 23-4

a

b

R

L

II

R

(a) I0 = 0 (b) I0 = / 2R (c) I0 = 2 / R

What is the value of the current I0

immediately after the switch is

thrown?

C: 23-5

Lecture 24

At t=0, the switch is thrown from position b to position a as shown:

– Let tI be the time for circuit I to reach 1/2 of its asymptotic current.

– Let tII be the time for circuit II to reach 1/2 of its asymptotic current.

– What is the relation between tI and tII?

R

a

b

L

I I

R

a

b L

I I

R

L

I

II (a) tII < tI (b) tII = tI (c) tII > tI

C: 24-1

Lecture 25

At t=0, the capacitor in the LC circuit shown has a total charge Q0. At t = t1, the capacitor is uncharged.

– What is the value of Vab, the voltage across the inductor at time t1?

(a) Vab < 0 (b) Vab = 0 (c) Vab > 0

LC

LC

+ +

- -Q 0Q Q 0

t=0 t=t1

a

b

C: 25-1

At t=0, the capacitor in the LC circuit shown has a total charge Q0. At t = t1, the capacitor is uncharged.

What is the relation between UL1, the energy stored in the inductor at t =

t1, and UC1 , the energy stored in the capacitor at t = t1?

(a) UL1 < UC1 (b) UL1 = UC1 (c) UL1 > UC1

LC

LC

+ +

- -Q 0Q Q 0

t=0 t=t1

a

b

C: 25-2

(a) w2 = 1/2 w0 (b) w2 = w0 (c) w2 = 2 w0

LC

+ +

- -Q Q 0

t=0At t = 0 the capacitor has charge Q0; the resulting oscillations have frequency w0. The maximum current in the circuit during these oscillations has value I0 .

– What is the relation between w0 and w2 , the frequency

of oscillations when the initial charge = 2Q0 ?

C: 25-3

• At t = 0 the capacitor has charge Q0; the resulting oscillations have frequency w0. The maximum current in the circuit during these oscillations has value I0 .

What is the relation between I0 and I2 , the maximum current in

the circuit when the initial charge = 2Q0 ?

(a) I2 = I0 (b) I2 = 2 I0 (c) I2 = 4 I0

LC

+ +

- -Q Q 0

t=0

C: 25-4

LC+ +

- -

i

Q

At t = 0 the current flowing through the circuit is 1/2 of its maximum value.

– Which of the following is a possible value for the phase f, when the charge on the capacitor is described by: Q(t) = Q0cos(wt + f).

(a) f = 30° (b) f = 45° (c) f = 60°

C: 25-5

Lecture 26

• At t = 0 the current flowing through the circuit is 1/2 of its maximum value.

– Which of the following plots best represents UB, the energy stored in the inductor as a function of time ? LC

+ +

- -

i

Q

(a) (b) (c)

x ..,0r1

nr1

0 2 4 60

0.5

1

f( )x

x

0 2 4 60

0.5

1

f( )x

x

x ..,0r1

nr1

0 2 4 60

0.5

1

f( )x

x

0 0

UB

time

0 0

UB

time

0 0

UB

time C: 25-6

Series LCR circuit is driven by a generator with = msinwt. The time dependence of the current i which flows in the circuit is shown in the plot.

– How should w be changed to bring the current and driving voltage into phase?

(a) increase w (b) decrease w (c) impossible

LC

R

X LL w XC

C 1

w

0

x ..,0r1

nr1

2 4 61

0

11.01

1.01

f( )x

6.81.53 x

io

im

-im0

i

t

x ..,0r1

nr1

0 2 4 61

0

1

f( )x

x

• The primary coil of an ideal transformer is connected to an AC voltage source as shown. There are 50 turns in the primary and 200 turns in the secondary.

– If V1 = 120 V, what is the potential drop across the resistor R ?

(a) 30 V (b) 120 V (c) 480 V

N2

N1

(primary) (secondary)

iron

V2V1 R

• The primary coil of an ideal transformer is connected to an AC voltage source as shown. There are 50 turns in the primary and 200 turns in the secondary.

N2

N1

(primary) (secondary)

iron

V2V1 R

– If 960 W are dissipated in the resistor R, what

is the current in the primary ?

(a) 8 A (b) 16 A (c) 32 A